Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#430 ⋊ C2 |
| Sylow | C7 ⋊ #2048 |
274 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^7,7|c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^6,c^b=cf,d^b=dg,h^b=h^6,f^c=fg89 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2048, C2×#11728490, #13381643, … |
| maximal normal subgroup of | D7×#2048, C2×#11728490, #13381643, … |
| maximal quotient of | #13257364, #13257371, #13257378, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3256);